Graphical Gaussian Process Models for Highly Multivariate Spatial Data

For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is undesirable, especially for highly multivariate settings, where popular cross-covariance functions such as the multivariate Mat\'ern suffer from a "curse of dimensionality" as the number of parameters and floating point operations scale up in quadratic and cubic order, respectively, in the number of variables. We propose a class of multivariate "Graphical Gaussian Processes" using a general construction called "stitching" that crafts cross-covariance functions from graphs and ensures process-level conditional independence among variables. For the Mat\'ern family of functions, stitching yields a multivariate GP whose univariate components are Mat\'ern GPs, and conforms to process-level conditional independence as specified by the graphical model. For highly multivariate settings and decomposable graphical models, stitching offers massive computational gains and parameter dimension reduction. We demonstrate the utility of the graphical Mat\'ern GP to jointly model highly multivariate spatial data using simulation examples and an application to air-pollution modelling

Bayesian modeling with spatial curvature processes

Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied response. We develop Bayesian modeling and inference for rapid changes on the response surface to assess directional curvature along a given trajectory. Such trajectories or curves of rapid change, often referred to as \emph{wombling} boundaries, occur in geographic space in the form of rivers in a flood plain, roads, mountains or plateaus or other topographic features leading to high gradients on the response surface. We demonstrate fully model based Bayesian inference on directional curvature processes to analyze differential behavior in responses along wombling boundaries. We illustrate our methodology with a number of simulated experiments followed by multiple applications featuring the Boston Housing data; Meuse river data; and temperature data from the Northeastern United States

Graph-constrained Analysis for Multivariate Functional Data

Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many applications of multivariate functional data, the graph is known and existing functional GGM methods cannot preserve a given graphical constraint. In this manuscript, we demonstrate how to conduct multivariate functional analysis that exactly conforms to a given inter-variable graph. We first show the equivalence between partially separable functional GGM and graphical Gaussian processes (GP), proposed originally for constructing optimal covariance functions for multivariate spatial data that retain the conditional independence relations in a given graphical model. The theoretical connection help design a new algorithm that leverages Dempster's covariance selection to calculate the maximum likelihood estimate of the covariance function for multivariate functional data under graphical constraints. We also show that the finite term truncation of functional GGM basis expansion used in practice is equivalent to a low-rank graphical GP, which is known to oversmooth marginal distributions. To remedy this, we extend our algorithm to better preserve marginal distributions while still respecting the graph and retaining computational scalability. The insights obtained from the new results presented in this manuscript will help practitioners better understand the relationship between these graphical models and in deciding on the appropriate method for their specific multivariate data analysis task. The benefits of the proposed algorithms are illustrated using empirical experiments and an application to functional modeling of neuroimaging data using the connectivity graph among regions of the brain.Comment: 23 pages, 6 figure

Synthesis, characterization and catalytic properties of multinuclear copper(II) complexes

Four tetranuclear [Cu4(O)(Ln)2(CH3COO)4] (1, 2, 4 and 5) and one pentanuclear [Cu5(OH)2(L3)2(CH3COO)6] (3) with N2O-donor Schiff-base ligands have been synthesized, where HL1= 4-methyl-2,6-bis(2-hydrox- yethyliminomethyl)phenol for complex 1, HL2= 4-methyl-2,6-bis(3-hydroxypropyliminomethyl)phenol for complex 2, HL3= 4-methyl-2,6-bis(4-hydroxybutyliminomethyl)phenol for complex 3, HL4= 4-methyl-2,6-bis(5-hydroxypentyliminomethyl)phenol for complex 4 and HL5= 4-methyl-2,6-bis (6-hydroxyhexyliminomethyl)phenol for complex 5. These complexes have been characterized by elemental analysis, FT-IR, UV–Vis spectroscopy. The structures of 1, 3, 4 and 5 have been determined by single crystal X-ray diffraction studies. X-ray analysis reveals that complexes 1, 4 and 5 are l4-oxido-bridged tetrameric copper(II) complexes, where four copper atoms arrange themselves around an oxidooxygen atom at the vertices of a distorted tetrahedron. The pentanuclear complex, 3, has been found to have two l3-hydroxido bridging ligands each connecting three copper atoms. These complexes have been employed as catalyst for the epoxidation of olefins in the presence of tert-butyl hydroperoxide (TBHP) as the oxidant under mild conditions

Synthesis, characterization and DFT calculations of N,O Schiff base complex of copper(II)

1451-1458<span style="font-size:11.0pt;mso-bidi-font-size: 10.0pt;font-family:" times="" new="" roman";mso-fareast-font-family:calibri;="" mso-bidi-font-family:"times="" roman";mso-ansi-language:en-gb;mso-fareast-language:="" en-us;mso-bidi-language:ar-sa"="" lang="EN-GB">M<span style="font-size:11.0pt; mso-bidi-font-size:10.0pt;font-family:" times="" new="" roman";mso-fareast-font-family:="" "times="" roman";mso-bidi-font-family:"times="" roman";mso-ansi-language:="" en-gb;mso-fareast-language:en-us;mso-bidi-language:ar-sa"="" lang="EN-GB">ononuclear copper(II) complex of the Schiff base, 2-methoxy-6-(3-morpholinopropyl-iminomethyl) phenol, [Cu(HL)2](ClO4)2].H2O (1) has been synthesized and characterized by elemental analysis and different spectroscopic techniques. The structure of (1) is confirmed by single crystal X-ray diffraction analysis. The complex (1) crystallizes in the monoclinic space group P21/n. The crystal structure of the mononuclear complex exhibits two Schiff base ligands bound to the copper atom and two perchlorate ions as non-coordinating species. Both the ligands in (1) are zwitterions where nitrogen atom of the morpholine ring is protonated. Fluorescence spectral study shows that HL displays an emission band at 535 nm on excitation at 418 nm. The presence of Cu2+ ion in complex (<b style="mso-bidi-font-weight: normal">1) quenches its emission intensity. DFT and TDDFT calculations have been carried out to investigate the spectral transitions.</span

Synthesis, characterization and DFT calculations of N,O Schiff base complex of copper(II)

Mononuclear copper(II) complex of the Schiff base, 2-methoxy-6-(3-morpholinopropyl-iminomethyl) phenol, [Cu(HL) 2 ](ClO 4 ) 2 ].H 2 O (1) has been synthesized and characterized by elemental analysis and different spectroscopic techniques. The structure of (1) is confirmed by single crystal X-ray diffraction analysis. The complex (1) crystallizes in the monoclinic space group P21/n. The crystal structure of the mononuclear complex exhibits two Schiff base ligands bound to the copper atom and two perchlorate ions as non-coordinating species. Both the ligands in (1) are zwitterions where nitrogen atom of the morpholine ring is protonated. Fluorescence spectral study shows that HL displays an emission band at 535 nm on excitation at 418 nm. The presence of Cu 2+ ion in complex (1) quenches its emission intensity. DFT and TDDFT calculations have been carried out to investigate the spectral transitions

A turn-on fluorescent chemosensor for Zn2+ ion: X-ray structure and application in cell imaging study

The selective fluorescence zinc(II) sensing properties of a Schiff-base compound, 2-methoxy-6-(2-morpholinoethyliminomethyl)phenol (HL) have been explored. The emission intensity of HL in the presence of one equivalent of Zn2+ ion increases by about 25 times. Several other metal ions, except Cd2+ and Ni2+, have not been able to increase the emission intensity of HL significantly. The quantum yield and life-time of HL have also been increased in the presence of Zn2+ ions. The enhancement in fluorescence intensity of HL is mainly due to the restriction of ESIPT, CHEF and PET on complex formation. HL forms a complex with Zn2+ in 1:1 ratio as evidenced by Job's plot analysis and X-ray single crystal structure determination. Some theoretical calculations have been performed to get a better view on the nature of the observed electronic transitions. The probe has been applied for imaging of DLD-1, human colorectal adenocarcinoma cell

Effect of chain length and donor–acceptor substitution on the electrical responsive properties of conjugated biphenyls: a DFT-based computational study

<p>The effect of donor–acceptor (D-A) substituent and chain length on the electrical polarisabilities and first hyper polarisability of cis and trans biphenyl oligomeric compounds have been investigated using density functional theory-based hybrid functional CAM-B3LYP with 6-311G (2d,2p) basis set. Our extensive computational study reveals that both average polarisability and first hyper polarisability of the studied compounds increase with the increasing ethylene spacer chain length. Again the substitution of donor (NMe₂) and acceptor (C≡N) at the para position of the phenyl rings to each oligomer shows order of magnitude increase of both <i>α</i>_av and <i>β</i>_av value compared to the unsubstituted one. This increased <i>α</i>_av and <i>β</i>_av values have been explained due to increasing charge transfer contribution resulting from decreasing optical energy gap (Δ<i>E</i> = <i>S</i>₁ − <i>S</i>₀) upon D-A substitution. It is also observed that the charge transfer contribution to first hyperpolarisability (<i>β</i>_CT) is more than the polarisability (<i>α</i>_CT) for the studied molecules. The electronic spatial extent (<<i>R</i>²>) which is a measure of electron density volume around the molecule is found to play a major role along with the intramolecular charge transfer character to explain the non-linear variation of first hyperpolarisability (<i>β</i>_av) as a function of ethylene spacer chain length (<i>n</i>) and D-A substitution.</p